Let $F$ be a 2D vector field. Is the expression $\text{div}(\text{curl}(F))$ a scalar field, a vector field, or undefined? Choose 1 answer: Choose 1 answer: (Choice A) A Scalar field (Choice B) B Vector field (Choice C) C Undefined
Answer: The divergence, which takes a vector field and gives a scalar field, can be written in two ways: $\text{div}(F) = \nabla \cdot F$ The 2D curl, which takes a vector field and gives a scalar field, can be written in two ways: $\text{curl}(F) = \nabla \times F$ Therefore, $\text{div}(\text{curl}(F))$ is the divergence of the curl of a 2D vector field. The curl of a 2D vector field is a scalar field. Because the divergence only takes vector fields, the divergence of a scalar field is undefined. The expression $\text{div}(\text{curl}(F))$ is undefined.